"My hair was so greasy that I couldn't help but WASH it. Since I HAD ran out of shampoo THOUGH, I had to wash my hair with soap INSTEAD." Above are my corrections to your sentence to make it 100% natural: --> I changed "washing it" to "wash it" because -ing verbs are for current actions only. --> I removed "well" because it is not correctly used in this sentence. --> I added "had" to indicate the past situation having already occurred. --> I added "though" to indicate that the 2nd phrase had a negative in it, unlike the first sentence. --> I added "instead" to show you replaced one thing with another (shampoo with soap). The word "well" is used as follows: "I had to go to the well" --> a noun to indicate the place you get water from deep within the ground "His job is not going well" --> an adverb to indicate a positive outcome. "I am quite well thanks" --> an adjective to indicate good health. "Well I guess we could do that" --> an exclamation to indicate hesitation before concluding a topic. "Well? What do you think?" --> an exclamation to indicate that you are expecting an answer.

"Well" seems OK to me here. In speech, you could also use things like "but" or "so". In writing, you could use something like "however." In general, English uses conjunctions and conjunctive adverbs a bit less often than East Asian languages do, but I agree that here it sounds a bit better to use one.

To Stacey : thank you so much! To Gary : I don't know for sure what my sentence means. I am just feeling like 'well' is very natural for me as a foreigner because our language needs 'well' very often between the sentences. But at the same time, from what I learn but I can't remember exactly, I guess it could be wrong and be replaced with something. So I want to check only 'well'

Is this your sentence? Or one you want to change?

Only two minor changes for it to sound more natural: My hair was so greasy that I couldn't help but wash it. Since I had ran out of shampoo I had to wash it with soap.